The Dynamics in Biology Seminar presents “Global stability of triatomine re-infestation models and a centrality measure for maps” on Tuesday, Nov. 17, at 5:10 p.m. in Morton 313.
The speakers are Ohio University graduate students Bismark Oduro (Mathematics) and Philip Miller (Biology Sciences).
Abstract: Chagas disease is a major health problem in rural South and Central America where an estimated 8 to 11 million people are infected. It is a vector-borne disease transmitted to humans mainly through the bite of insect vectors from the family of triatomines, also called “kissing bugs.” One of the control measures is insecticide spraying of homes to prevent infestation by the vectors. However, re-infestation of homes by vectors has been shown to occur as early as four to six months after insecticide spraying.
The first part of this talk will briefly introduce ODE-based mathematical models of the effect of insecticide spraying on vector re-infestation. Then we will focus on deriving results about global stability of the equilibria by constructing Lyapunov functions for some of these models.
These models have three key rate parameters that need to be estimated from data. Available data include topographical maps of communities with information about which housing units are infested. We formulated a hypothesis on infestation patterns that could in principle allow disentanglement of rate of house-to-house infestation and the rate of infestation from sylvatic areas. Its mathematical involves a certain centrality measure. We will describe this measure and an ongoing effort to statistically confirm our hypothesis by analyzing a set of 63 maps with associated data on infestation.
Comments